1. Extracting Dense Regions From
HurricaneTrajectory Data[1]
Praveen KumarTripathi, Madhuri Debnath, Ramez Elmasri
Dept. of Computer Science, University ofTexas at Arlington
Presented By:
Vivek Kumar Sharma
[1]”GeoRich’14 Proceedings ofWorkshop on
Managing and Mining Enriched Geo-Spatial Data”

2. Outline
• Introduction
• Trajectory Clustering on Point Data
• DBSCAN
• Dense Regions Extraction
• Experiments and Analysis
• Related Work
• Conclusion
• References

3. Introduction
• Weather Data:A good example of Spatial-temporal data(Time & Space)
• Clustering: Key technique to analyze storm trajectories
• Trajectories, Sub-Trajectories and Point Data
• (long, lat) as spatial attributes and (wind-speed, time) as similarity measure
• Monitoring & Predicting Weather conditions
• Identifying origin, destination of Hurricanes and most affected regions
• Hurricane dataset in Atlantic region from 1950-1999 with attributes longitude,
latitude, time, wind-speed, pressure and status

4. Trajectory Clustering on Point Data
• Consider a trajectory as an individual Point
• Points are not constrained to belong to its respective parent trajectory or
sub-trajectory
[1] http://weather.unisys.com/hurricane/atlantic/2012H/index.php

5. DBSCAN
• Two global parameters:
• Eps: Maximum radius of the neighborhood
• MinPts: Minimum number of points in an Eps-neighborhood of that point
• Density = number of points within a specified radius r (Eps)
• Core Object: object with at least MinPts objects within a radius ‘Eps-neighborhood’
• Border Object: object that on the border of a cluster
• A noise point is any point that is not a core point or a border point.

6. Background (I)
• NEps(p): {q belongs to D | dist(p, q) <= Eps}
• Directly density-reachable:
A point p is directly density-reachable from a point q wrt. Eps, MinPts if
• 1) p belongs to NEps(q)
• 2) |NEps (q)| >= MinPts
(core point condition) p
q
MinPts = 5
Eps = 1 cm

7. Background (II)
• Density-reachable:
• A point p is density-reachable
from a point q wrt. Eps, MinPts if
there is a chain of points p1, …,
pn, p1 = q, pn = p such that pi+1 is
directly density-reachable from
pi
• Density-connected:
• A point p is density-connected
to a point q wrt. Eps, MinPts if
there is a point o such that both,
p and q are density-reachable
from o wrt. Eps and MinPts.
p
q
p1
p q
o

8. DBSCAN Algorithm
• Arbitrary select a point p
• Retrieve all points density-reachable from p wrt Eps and MinPts.
• If p is a core point, a cluster is formed.
• If p is a border point, no points are density-reachable from p and DBSCAN visits the next
point of the database.
• Continue the process until all of the points have been processed.
Core
Border
Outlier
Eps = 1cm
MinPts = 5

9. Dense Region Extraction
• How to find regions of high storm activity
• DBSCAN parameter Eps which gives the neighborhood
• First neighborhood considering spatial attributes
• Then adding non-spatial measure wind-speed as well
• SpatialClustering
• Spatial and non spatial clustering
• Spatial temporal clustering

10. Dense Region Extraction
(Spatial Clustering)
• Latitude and Longitude as data points
• Haversine formula as similarity measure between two points
• a = sin(/2) + cos(φ1) × cos(φ2) × sin2(λ/2)
• c = 2 × arctan 2(pa, p(1 − a))
• d = R × c
• where (φ/latitude) = φ2 − φ1 and (λ/longitude) = λ2 − λ1, R = 6371Km is the radius of the
Earth, and d is the Haversine distance.
• This formula is used to calculate spherical distance between two points because of
spatial coordinates which are lying on spherical object(Earth)

11. Dense Region Extraction
(Spatial and non Spatial Clustering)
• Extending DBSCAN to handle non-spatial attribute
• If we have a data set D = {d1, d2, . . . , dn}, where di = (xi, yi, ai, bi) and (xi, yi) be the
spatial attribute & (ai, bi) as non-spatial attribute
• Similarity measure can be calculated as:
• dist_spatial (d1,d2) = √(x1 − x2)^2 + (y1 − y2)^2
• dist_nonspatial (d1,d2) = √(a1 − a2)^2 + (b1 − b2)^2
• Remaining steps for DBSCAN will remain same to calculate dense regions for
spatial and non-spatial attributes
• Finally composite neighborhood will include data points common in both

12. Dense Region Extraction
(SpatialTemporal Clustering)
• Consider Time as non-spatial attribute for analysis
• Hurricane data is sampled at 6 hour interval
• Haversine formula is being used to calculate similarity measure between spatial
attributes of two data points
• Manhattan distance for non-spatial attribute time is used
• Relative time framework instead of Absolute time considered which means relative
time from start of a particular trajectory
• Important to analyze movement patterns of hurricane
• Normalized time component(as per length of trajectory) varies between 0-1.0
• 0.00 signifies initial stage
• 0.5 signifies middle stage
• Higher values close to 1.0 signifies end of hurricane

13. Experiments and Analysis
• Implementation and Analysis being done on MATLAB
• Different combinations of Eps and MinPts has been tried to get well
separated and compact clusters
• Four different types of analysis being done:
• Analysing Spatial attributes
• QualitativeAnalysis of clusters
• Analysing combination of spatial and non-spatial attributes
• Storm starting and landing information

14. Experiment and Analysis
(Analysing Spatial Attributes)
• Eps= 35, MinPts= 10, k= 15

15. Experiment and Analysis
(Qualitative Analysis of Clusters)
• Clustering based on spatial and non-spatial attributes
• Wind-speed and Time
• Wind-speed threshold has been varied from 20-100 in the interval of 10
• Time/Temporal threshold from 0.2-1.0 in the interval of 0.1
• Quality measure needed to check the clustering results
• SSE= (Sum of the Square Error)
• numclus is the number of clusters, N is the set of noise points and Ci is the ith cluster
• Smaller the value of SSE, better will be the clustering results

16. Experiment and Analysis
(Combination of Spatial and non-spatial attributes)
• Studying the nature of storms
• Now neighboring points will be close to core data point spatially and will
have similar wind-speed values
• Reduced cluster size as they represents regions with same nature of storms
• As wind-speed being reduced cluster size also reduces

17. Experiment and Analysis
(Combination of Spatial and non-spatial attributes)
• SSE Results :
• Reduction in wind-speed results
compact and homogeneous
clusters.
• Spatial-Temporal Clustering:
• Temporal threshold reduced
from 1.0 to 0.2.

18. Experiment and Analysis
(Storm Starting and Landing Information)
• Storm Starting Clusters
• Considered starting three data points wrt first
three timestamps for each trajectory
• Storm Landing Clusters
• Considered last three data points

19. RelatedWork
• DENTRAC (DENsity basedTRAjectory Clustering)
• Post processing of clusters to get more domain specific knowledge
• Partition and Group based Clustering
• Using concept of MDL (Minimum Descriptive Length) identifies characteristic points
• Representing trajectory by connecting consecutive characteristics points
• Clustering algorithm using computational geometry and string processing
• Remove noise by preprocessing trajectory data and divide into sub-trajectories
• Slicing-STS-Miner using sequential patterns
• Spatial temporal pattern convoy being proposed
• Region based &Trajectory based Clustering
• Classifying trajectories using duration of trajectory as an important feature

20. Conclusion
• Analyzed hurricane trajectory data as point data
• Initial clustering based on spatial attributes
• Influence of non-spatial attribute i.e. wind-speed obtained
• Spatial temporal DBSCAN algorithm has been proposed in which
normalized time is also considered as non-spatial attribute
• Post-processing of clusters to get origin, landing and tracking information

21. References
• http://weather.unisys.com/hurrricane/atlantic/index.html.
• Data Mining: Concepts andTechniques, 2nd ed.Morgan Kaufmann, 2006.
• Derya Birant and Alp Kut. ST-DBSCAN:An algorithm for clustering spatial-temporal data. DataKnowl.
Eng., 60(1):208–221, January 2007.
• Chun-Sheng Chen, Christoph F. Eick, and NouhadJ. Rizk. Mining spatial trajectories using non-
parametric density functions. In Petra Perner, editor, Machine Learning and Data Mining in Pattern
Recognition,volume 6871 of Lecture Notes in Computer Science, pages 496–510. Springer Berlin
Heidelberg, 2011.
• Martin Ester, Hans peter Kriegel, Jorg S, and Xiaowei Xu. A density-based algorithm for discovering
clusters in large spatial databases with noise. pages 226–231.AAAI Press, 1996.
• Jae gil Lee and Jiawei Han.Trajectory clustering:A partition-and-group framework. In In SIGMOD,
pages 593–604, 2007.

22. References
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